Caroline Wozniacki of Denmark returns the ball to Nuria Llagostera...

Caroline Wozniacki of Denmark returns the ball to Nuria Llagostera Vives of Spain during the first round of play at the U.S. Open in Forest Hills, NY (Aug. 30, 2011) Credit: Kathleen Malone-Van Dyke

So, she lost a couple of first- round matches this summer. So, she's No. 1 in the world without having won a major tournament. So, she now has a "mystery coach" she won't reveal.

None of this matters particularly to Caroline Wozniacki. There is a reason she's earned the nickname "Sunshine."

On a blazingly bright day at Arthur Ashe Stadium, Wozniacki dispatched the diminutive Nuria Llagostera Vives, 6-3, 6-1, Tuesday to begin another drive for her first major title at the place she made her first major statement.

Two years ago, she reached the final of the U.S. Open, her only Grand Slam final appearance, and lost to Kim Clijsters. That's the furthest she's ever gone in a Slam. But her consistency, her ability to win other tournaments, has carried her to No. 1 in the world, a position she's held since October with the exception of one week in February. She's won six tournaments this year, including a fourth consecutive New Haven Open title last week. She considers herself in "match mode," with all her good tennis bubbling up. She's on a high.

"I mean, why shouldn't it be high?" the Dane said. "I'm No. 1 still and just won a tournament, so I'm feeling fine. Again, I just lost two matches . That happens. I just won four in a row, this is my fifth one. I'm feeling OK."

Though without a Grand Slam win or final appearance this season, she has been consistently topnotch. She's won a top-tier tournament at Indian Wells, along with titles at New Haven, Dubai, Charleston, Brussels and Copenhagen. She made the semifinals at the Australian Open, the fourth round at Wimbledon, the third round at the French Open. She did rather glaringly lose first-round matches to Roberta Vinci at Toronto and Christina McHale at Cincinnati, both hardcourt events. Vives, her Spanish opponent Tuesday who looked barely bigger than her racket at 5-1½, never threatened to make Wozniacki a first-round loser for the third time this year.

While piling up enough points to be No. 1, Wozniacki still has some work to do to be a major winner. She talked with Martina Navratilova about helping her earlier this season, but the details couldn't be worked out.

Her father, Piotr, her lifelong coach, acknowledged that a "mystery coach" has become part of Wozniacki's team, apparently someone who looks at her technically from afar on video and makes suggestions.

"I have to respect him as well," Wozniacki said. "So if he wants to be in the background and not have his name out, I have to respect that."

This technical adviser has been providing a few tidbits before the Open. "Even yesterday," Wozniacki said. "He's been watching me and telling me a few things. It's working well."

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